Also cost does come in play as well. Multiple physical links in would be very expensive for what sounds like internal services. Likewise a natural disaster might cause bigger issues to the company than those internal services going down. They might still have offsite back ups (I'd hope they would!) so at least they can recover the services but the cost of having a live redundancy system off site might not justify those risk factors.
The customers requires are definitely unreasonable though. I'd hope those systems are regularly patched, in which case when is downtime for that scheduled and why is that acceptable but not when you're physically moving the server? I doesn't really make much sense; but then "not making much sense" also quite a common problem when providing IT services for others.